The value of the determinant b2 - ab b - c bc - ac ab - a2 a - b b2 - ab bc - ac c - a ab - a2

The correct option is C 0 b^2 ab #160; amp; b c #160; amp; bc ac ab a^2 #160; amp; a b #160; amp;b^2 ab #160; ...

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Addition and Subtraction of a Matrix

The value of ...

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The value of the determinant $∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣$

a b c

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a + b + c

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0

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a b + b c + c a

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∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ =

∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ =

|\begin{matrix} b^{2} - a b & b - c & b c - a c \\ a b - a^{2} & a - b & b^{2} - a b \\ b c - c a & c - a & a b - a^{2} \end{matrix}|

a b c (b - c) (c - a) (a - b)

(b - c) (c - a) (a - b)

(a + b + c) (b - c) (c - a) (a - b)

∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + b^{2} + c^{2} & b c + c a + a b & b c + c a + a b b c + c a + a b & a^{2} + b^{2} + c^{2} & b c + c a + a b b c + c a + a b & b c + c a + a b & a^{2} + b^{2} + c^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

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